Abstract
We consider the inertial Qian–Sheng’s Q-tensor dynamical model for the nematic liquid crystal flow, which can be viewed as a system coupling the hyperbolic-type equations for the Q-tensor parameter with the incompressible Navier–Stokes equations for the fluid velocity. We prove the existence and uniqueness of local in time strong solutions to the system with the initial data near uniaxial equilibrium. The proof is mainly based on the classical Friedrich method to construct approximate solutions and the closed energy estimate.
Highlights
1 Introduction Liquid crystals present a state of matter with properties between liquid and solid
4 Conclusions In this paper, we are mainly concerned with the inertial Qian–Sheng Q-tensor model describing the nematic liquid crystal flow
The inertial term J is responsible for the hyperbolic feature of the equation describing molecular orientation
Summary
Liquid crystals present a state of matter with properties between liquid and solid. The simplest form of liquid crystals is the nematic phase, which exhibits long-range orientational order but no positional order. There are two primary continuum theories to describe nematic liquid crystal flow: the Ericksen–Lesile theory and the Landau– de Gennes theory In the former one, the local alignment of molecules is described by a unit vector, which completely neglects molecular details. In the Landau–de Gennes framework, there exist two representative Q-tensor models, directly derived by a variational method, describing the hydrodynamics of nematic liquid crystals: the Beris–Edwards model [3] and the Qian–Sheng model [16]. During the physical modeling process, the liquid crystal system is not generally isotropic but certain nonzero uniaxial or biaxial equilibrium at infinity. 3, based on the classical Friedrich method and the closed energy estimate, we prove the local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model, when the solution to the system tends to the uniaxial equilibrium state at infinity.
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